Problem 2. Find all equilibrium points and determine the type of each isolated equilibrium. Verify with phase portrait. x, = (x, – x, X1 – x² – x}) i, = (x, + x, X1 – x} – x;) | |

Q: 2. Differentiate the following. Simplify your derivatives as much as possible. f(x)= (3x² – 4) |b)…

A: As per our company guidelines we can answer only three subpart question at a time so if you nee more…

Q: Let h(x)=f(g(x)). If f(−4)=−3, f′(−4)=−1, g(1)=−4, and g′(1)=3, find h′(1).

A: The formula one have to use here is f(g(x))'=f'(g(x))* g'(x)

Q: x3 C. g(x) : et

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Q: Determine which of the following pairs of functions are linearly independent. 1. f(t) = 3t, g(t) =…

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Q: If f(x) is a linear function, f( – 5) = - 5, and f(5) = – 3, find an equation for f(x) Submit…

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Q: A) Find the first and second derivatives of the function g(x) = Vx² + 2x .

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The temperature of a chemical reaction oscilllates between a low of 40 degreesC and a high of…

A: Solution :  Given ,  The temperature of a chemical reaction oscilllates between a low of 40 degreesC…

Q: 4. Examine if functions f(x)= x , f2 (x) = x², f;(x)=x² – 2x are linearly independent.

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Q: Find y as a function of t if y(0) = 5, y(0) = 3. y(t) = 36y" - 84y +58y = 0₂

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Q: Determine which of the following pairs of functions are linearly independent. 1. f(x) = x² g(x) =…

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Q: 1. f(x) = x² 9 2. f(0) = cos(30) g(x) = 4|x|² 3. f(t) = et cos(ut) 4. f(x) = e³x 9 9 9 g(0) = 12…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.